Any useful physical structure, device or material (hereinafter “structure”) must be adapted so that the structure can withstand the forces that are applied to the structure. In building architecture it is often a structural design principle to provide the greatest strength for the least size or weight as is practical. If followed, this principle can enable structures to be larger, more economical and more aesthetically pleasing.
The same principle is often useful in the design of materials used in a wide variety of applications other than buildings. Achieving a high strength-to-weight ratio is also important in the design of materials for aircraft, other vehicles, and almost any portable or movable object.
A leap forward in structural design was made in the early 1950's by Buckminster Fuller who invented what is commonly known as the geodesic dome, described in U. S. Pat. No. 2,682,235. Fuller showed how one could obtain a high strength-to-weight ratio in a domed structure through the orderly subdivision of the twenty equilateral spherical triangles of the icosahedron by arcs of great circles of the basic sphere, and interconnecting a plurality of struts representing the sides of the triangles that result from that subdivision. Due to the stable nature of triangular structures in response to stress, and assuming that the elastic limit of the strut material is not exceeded, the structure is able to support both itself and a relatively large load compared to its weight, and to provide a small ratio of structural weight-to-area covered, and volume enclosed, by the structure.
In the '235 patent, Fuller also described how, by employing two concentric, virtual spherical surfaces and forming tripods, or tetrahedral units, between them, one-half the struts could be replaced by tensional (hereunder “tension”) members such as wires or cables, the remaining struts ordinarily being in compression. Thus, Fuller introduced the idea of balancing the forces on interconnected, columnar compression members with interconnected, flexible tension members to produce a high strength-to-weight ratio truss forming a domed structure.
Later, Fuller introduced the idea of “tensegrity” (a combination of “tensile” and “integrity”), as described in his U.S. Pat. No. 3,063,521. Here, he showed that an even greater strength-to-weight ratio can be achieved by disconnecting the compression members from one another and eliminating more of them, the compression members being entirely interconnected by tension members. He referred to the remaining compression members as “discontinuous compression columns” because no compression force is transmitted directly from one column to another as they “float in a sea of tension elements.” Column 3, lines 57-59. He also showed how a basic three-strut tensegrity unit can be used to construct the geodesic dome for which he is well known.
In U.S. Pat. No. 3,354,591, Fuller extended his ideas to octahedral tensegrity modules whose edges are defined by tension members attached to the ends of interior compression members. The modules were joined face-to-face to produce a building truss. However, as pointed out by Kitrick in his U.S. Pat. No. 4,207,715, when the octahedral modules are so joined, the adjoining tension elements become redundant and one of each pair of such tension elements can be eliminated. This reduces the ratio of tension to compression-elements, which may be undesirable.
Kitrick suggests using any of octahedral, tetrahedral, or icosahedral modules, but adjoining the adjacent triangular faces in overlapping but inverse relation. Thus, Kitrick sought to eliminate the redundancy of tension elements, which might be advantageous in some circumstances, while adhering to the concept of columnar compression members discontinuously interconnected by tension members. At the same time, whether such a structure should be characterized as exhibiting tensegrity, because it lacks continuous tension, and second whether icosahedrons can effectively be arranged in the manner suggested.
Of the five regular Platonic polyhedra, namely the tetrahedron (4 equilateral triangles, 6 edges and 4 vertices), the cube (6 squares, 12 edges and 8 vertices), the octahedron (8 equilateral triangles, 12 edges and 6 vertices), the dodecahedron (12 regular pentagons, 30 edges and 20 vertices), and the icosahedron (20 equilateral triangles, 30 edges and 12 vertices), the dodecahedron and the icosahedron are the most complex and, unlike the other three, have five-fold symmetry. Nonetheless, the icosahedron, three pairs of whose faces may be arranged to be parallel to one another, has inspired various structures. As already mentioned, a spherical icosahedron was the starting point for the geodesic dome. Also Kitrick endeavored seemingly unsuccessfully to describe a structure made of icosahedral tensegrity modules.
In addition, Baer U.S. Pat. No. 3,722,153 and Hogan U.S. Pat. No. 3,953,948 disclose truss systems based on the icosahedron, and interleaved construction elements based on various polyhedrons, including the icosahedrons. However, none of these suggests the use of the tensegrity concept.
Characteristics of structural materials in addition to their strength-to-weight ratio may also be important to a particular application. Such characteristics may include, for example, optical, acoustical, electrical and chemical properties. While these properties may simply derive from the substance of which a structural material is made, they may also derive from a geometry, or a combination of substance and geometry. For example, much attention has been given to the potential of the carbon-60 molecule (commonly known as the “Buckyball”) due to its unusual geometry that may have unique useful properties, but the molecule so far mainly appears to have been a subject of scientific curiosity and research.
The afore-described works of Fuller on tensegrity structures, while groundbreaking and visionary, and the work of Kitrick, were confined in their scope to the use of columnar compression members in tensegrity structures used in building architecture. In addition, the Fuller structures are based on spherical symmetry, which does not lend itself well to fabricating structures with Cartesian or orthonormal symmetry. While the structures described by Kitrick are better adapted to fabricate structures with Cartesian symmetry, it turns out that they do not maximize the strength-to-weight ratio and are not readily scalable. Nor do any of these disclosures explore other properties that may be important, particularly in structural materials for applications other than building architecture.